标题：Backward stochastic optimal control with mixed deterministic controller and random controller and its applications in linear-quadratic control
作者：Zhang, Huanjun; Yan, Zhiguo
作者机构：[Zhang, Huanjun; Yan, Zhiguo] Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China.; [Yan, Zhiguo] Qilu Univ Technol, Shan 更多
通讯作者：Zhang, Huanjun;Zhang, HJ
通讯作者地址：[Zhang, HJ]Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China.
来源：APPLIED MATHEMATICS AND COMPUTATION
关键词：Backward stochastic differential equation; Feedback expression of; optimal control; Mean-field; Mixed deterministic and random control
摘要：This paper investigates an optimal control problem driven by backward stochastic differential equation (BSDE) with two controllers - one is called deterministic controller and the other one is called random controller. Necessary and sufficient conditions for the mixed optimal control problem are derived. A linear-quadratic (LQ) case of the mixed optimal control problem is also studied. The mixed optimal controllers are explicitly expressed by the solution of a fully coupled mean-field forward-backward stochastic differential equation (SDE). One of novel features is that a kind of mean-field BSDE naturally arises from the research on the mixed optimal control problem. Finally, a product management problem is used to illustrate the theoretical results. (C) 2019 Elsevier Inc. All rights reserved.